Dealing with Rebound Migraines and Strange Treatment Options

So… I ended up getting rebound migraines from the sumatriptan pills that I was prescribed and my neurologist told me to not take them anymore … she wants to put me on a treatment that is also treated for dementia … which is strange I don’t understand why I need to take dementia pills… also I’m currently having a headache because I haven’t taken suma nor did I take an over the counter pill. It’s the first day I’m not taking any pills. I’m wondering if I just rest this off if my headaches will get better in time again? I’m just concerned if the over the counter pill will cause a rebound headache too